If P = {3, 5, 6} and Q = {4, 5, 6} then P∩Q equals
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(D)
{5, 6}
3
A and B are two sets. The number of elements in A∪B is 49, the number in A is 22 and number in B is 34. How many elements are in A ∩ E?
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(E)
7
4
A student found the approximate value of 0.02548 correct to two places of decimal instead of two significant figures. Find the percentage error.
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(E)
20%
5
Simplify log39 + log315 - log35
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(C)
3
6
Solve me equation: 2/3 (x + 5) = 1/4(5x - 3)
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(E)
7
7
Which of the following equations has its roots as 4 and -5?
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(D)
x2 + x - 20 = 0
8
Solve the equations: 4x -y = 11; 5x + 2y = 4.
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(D)
x = 2, y = -3
9
Make q the subject of the relation t = √(pq/r - r\(^2\)q)
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(A)
q = \(\frac{rt^2}{(p - r^3)}\)
10
P varies inversely as the square of W. When W = 4, P = 9. Find the value of P when W = 9
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(D)
16/9
11
If x varies over the set of real numbers, which of the following is illustrated in the diagram above?
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(B)
-2 < x ≤ 3
12
In the triangle XYZ , XM is the altitude from X to YZ.XY = 13cm, XZ = 15cm and YM = 5cm. Find the length of YZ
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(C)
14cm
13
Two points P and Q are on longitude 67°W. Their latitudes differ by 90°. Calculate their distance apart in terms of π. (Take radius of the earth = 6400km).
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(C)
3200πkm
14
The length of the two parallel sides of trapezium are 6cm and 10cm and the perpendicular distance between them is 5cm. Find the area of the trapezium
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(B)
4Ocm2
15
Calculate the total surface area of a solid cone of slant height 15cm and base radius 8cm in terms of π
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(C)
184πcm2
16
The cross-section of a prism is a right-angled triangle 3cm by 4cm by 5cm. The height of the prism is 8cm. Calculate its volume
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(A)
48cm3
17
Find the radius of a circle in which an arc of length 44cm subtends angle 200° at the centre of the circle. [Take π = 22/7]
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(B)
12.6cm
18
The diagram above is a triangle XYZ whose area is 23.5cm2. XY =1Ocm and YZ = 8cm, calculate θ correct to the nearest degree.
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(C)
36o
19
Which of the following is not necessarily sufficient for the construction of a triangle?
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(C)
Two sides and a right angle
20
In the diagram, EF//QR, PE = 2cm, EQ = 4cm and FR = 6cm. Find x
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(B)
3cm
21
Which of the following statements is/are true when two straight lines intersect?
I. Adjacent angles are equal II. Vertically opposite angles are equal III. Adjacent angles are supplementary
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(C)
II and III only
22
PQRS and GHRS are parallelograms on the same base SR and between the same parallel straight line PH and SR. Which of the following is true?
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(E)
Parallelogram PQRS = Parallelogram GHRS
23
From the diagram above, which of the following is true?
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(D)
a + b = x + 180
24
The interior angles of a pentagon are 126o, 114o, y, 92o and 83o. Find the value of y.
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(E)
125o
25
Solve the inequality 3x - 8 ≥ 5x
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(C)
x ≤ -4
26
Divide 3.6721 by 4
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(A)
0.9180
27
The eleventh term of an AP, is 25 and its first term is -3. Find its common difference.
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(E)
24/5
28
Find the common ratio in the GP: log 3, log 9, log 81 ..........
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(B)
2
29
Find the value of t for which \(\frac{64}{27} = (\frac{3}{4})^{t - 1}\)
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(B)
-2
30
O is the centre of the circle PQRS. PR and QS intersect at T POR is a diameter, ∠PQT = 42o and ∠QTR = 64o; Find ∠QRT
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(A)
68o
31
TR is the tangent to the circle PQR with centre O. Find the size of ∠PRT
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(C)
60o
32
Given that \(\frac{1}{2} \log_{10} P = 1\), find the value of P.
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(C)
102
33
If two triangles are similar, which of the following is true? Their
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(B)
corresponding angles are equal
34
Which of the following is not necessarily true of a rectangle?
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(C)
The diagonals are perpendicular
35
A chord is 5cm from the centre of a circle of diameter 26cm. Find the length of the chord
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(C)
24cm
36
The angle of elevation of a point T on a tower from a point U on the horizontal ground is 30o. If TU = 54m, how high is T above the horizontal ground?
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(E)
27m
37
Express the true bearing of 250° as a compass bearing
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(D)
S70oW
38
lf sin θ= \(\frac{-1}{2}\), find all the values of θ between 0° and 360°.
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(D)
210o,330o
39
Cos 65o has the same value as
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(E)
Cos 295o
40
Two sides of a triangle are perpendicular. If the two sides are 8cm and 6cm, calculate correct to the nearest degree, the smallest angle of the triangle.
